Question:

A block of mass 5 kg is hanging from the ceiling by a string. The block is in equilibrium and its acceleration is zero.

(a) Calculate the tension force in the string.

(b) Now, suppose a person pushes the block upwards with a force of 30 N. Calculate the tension force in the string when the block is accelerating upwards at a rate of 2 m/s^2.

Use g = 9.8 m/s^2 for acceleration due to gravity.

Answer:

(a) To calculate the tension force in the string when the block is in equilibrium, we consider the forces acting on the block. These forces are the tension force in the string (T) and the gravitational force (mg) acting downwards.

Since the block is in equilibrium and its acceleration is zero, the net force acting on it must be zero.

Net force = T - mg = 0

Rearranging the equation, we get:

T = mg

Substituting the values, we have:

T = (5 kg)(9.8 m/s^2) T = 49 N

Therefore, the tension force in the string when the block is in equilibrium is 49 N.

(b) When the block is accelerating upwards at a rate of 2 m/s^2, we need to consider the additional force applied by the person pushing the block.

The net force acting on the block is given by:

Net force = T - mg + F_applied

Since the block is accelerating upwards, we have:

Net force = ma

Rearranging the equation, we can express T as:

T = mg + ma - F_applied

Substituting the values, we have:

T = (5 kg)(9.8 m/s^2) + (5 kg)(2 m/s^2) - 30 N T = 49 N + 10 N - 30 N T = 29 N

Therefore, the tension force in the string when the block is accelerating upwards at a rate of 2 m/s^2 is 29 N.